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  • Provide Solution for RD Sharma Class 12 Chapter Continuity Exercise 8.1 Question 10 Subquestion (ii)

Provide Solution for RD Sharma Class 12 Chapter Continuity Exercise 8 point 1 Question 10 Subquestion (ii)

Answers (1)

Answer:

                Continuous

Hint:

 For a function to be continuous at a point, its LHL RHL and value at that point should be equal.

Solution:

Given,

f(x)=\left(\begin{array}{c} x^{2} \sin \left(\frac{1}{x}\right), \text { if } x \neq 0 \\\\ 0 \quad, \text { if } x=0 \end{array}\right)

We observe

\begin{aligned} &\lim _{x \rightarrow 0} f(x)=\lim _{x \rightarrow 0} x^{2} \sin \left(\frac{1}{x}\right)=\lim _{x \rightarrow 0} x^{2} \lim _{x \rightarrow 0} \sin \left(\frac{1}{x}\right)=0 \times \lim _{x \rightarrow 0} \sin \left(\frac{1}{x}\right)=0 \\\\ &\lim _{x \rightarrow 0} f(x)=f(0) \end{aligned}

Hence,  f\left ( x \right ) is continuous at x=0.

 

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